Transcript Finding the Sum of a Polygon’s Interior Angles

Finding the Sum of a Polygon’s
Interior Angles
17 July 2015
Here are some polygons
The word
‘polygon’ is a
Greek word.
Poly means
many and
Triangle
Pentagon
Octagon
gon means
angles.
How to find the sum of the interior angles
– i.e. How to find a + b + c + d + e
b
a
c
e
d
How to find the sum of the interior angles
– i.e. How to find a + b + c + d + e
Split the shape up
into triangles
How to find the sum of the interior angles
– i.e. How to find a + b + c + d + e
Split the shape up
into triangles
1800
1800
1800
Each triangle
contains 1800
How to find the sum of the interior angles
– i.e. How to find a + b + c + d + e
Split the shape up
into triangles
1800
1800
Each triangle
contains 1800
3 x 180 = 5400
1800
How to find the sum of the interior angles
– i.e. How to find a + b + c + d + e
Split the shape up
into triangles
1800
1800
Each triangle
contains 1800
3 x 180 = 5400
1800
The sum of the
interior angles is
5400
Copy and complete this table. Find the
interior angles by drawing and splitting up
into triangles.
Name
Number Sum of Interior Angles
of Sides
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
Copy and complete this table. Find the
interior angles by drawing and splitting up
into triangles.
Name
Number Sum of Interior Angles
of Sides
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
900
Octagon
8
1080
Nonagon
9
1260
Decagon
10
1440
Regular Polygons
NB. If the
polygon is
regular, to
find an
interior angle
use the rule:
Interior Angle
1200
Int.Angle = 180 – (360 ÷ n)
n is the number of sides
Int. = 180 – (360 ÷ 6)  180 – 60 =120
Regular Polygons
NB. If the
polygon is
regular, to
find an
exterior angle
use the rule:
exterior angle
(180 – 120 = 60
Interior Angle
1200
Ext.Angle = 360 ÷ n
n is the number of sides
And Ext. Angle = 180 – Int.Angle